Space-Time Splitting and the Newtonian Limit in General Relativity Theory

Is there a well-motivated, mathematical separation of space and time in general relativity? Common approaches are either coordinate-dependent, require additional constraints and geometric structures, or are physically unjustified. As a remedy, we motivate an approach via individual observers and their past light cones, leading to the definition of `observer mappings'. The concept of a frame of reference is defined mathematically, tying sensibly to the general theory. Results include statements on the domain and smoothness of observer mappings, the relation between `actual' and `observed' causality, as well as the question of how the `observer spacetime' relates to the actual one. As the employed concepts of space and time need to reduce to the Newtonian ones in an approximation, the theory provides a natural framework for the Newtonian limit. For mass points, this translates to expanding an `equation of observed motion' in inverse powers of the speed of light. In this equation `actual' forces and pseudo-forces can generally be distinguished. For `inertial frames' in Minkowski spacetime, a pseudo-force exists due to the change of clock rate of the accelerated `observed observer'. In the zeroth order, the pseudo-force disappears and Newton's second law is indeed obtained.